Generalized spaces of double sequences for Orlicz functions and bounded-regular matrices over n-normed spaces

Gähler S: Linear 2-normierte Räume. Math. Nachr. 1965, 28: 1–43. Misiak A: n -Inner product spaces. Math. Nachr. 1989, 140: 299–319. 10.1002/mana.19891400121 Gunawan H: On n -inner product, n -norms, and the Cauchy-Schwartz inequality. Sci. Math. Jpn. 2001, 5: 47–54. Gunawan H: The space of p -summable sequence and its natural n -norm. Bull. Aust. Math. Soc. 2001, 64: 137–147. 10.1017/S0004972700019754 Gunawan H, Mashadi M: On n -normed spaces. Int. J. Math. Math. Sci. 2001, 27: 631–639. 10.1155/S0161171201010675 Hardy GH: On the convergence of certain multiple series. Proc. Camb. Philos. Soc. 1917, 19: 86–95. Bromwich TJ: An Introduction to the Theory of Infinite Series. Macmillan & Co., New York; 1965. Móricz F: Extension of the spaces c and c 0 from single to double sequences. Acta Math. Hung. 1991, 57: 129–136. 10.1007/BF01903811 Móricz F, Rhoades BE: Almost convergence of double sequences and strong regularity of summability matrices. Math. Proc. Camb. Philos. Soc. 1988, 104: 283–294. 10.1017/S0305004100065464 Başarır M, Sonalcan O: On some double sequence spaces. J. Indian Acad. Math. 1999, 21: 193–200. Mursaleen M, Mohiuddine SA: Regularly σ -conservative and σ -coercive four dimensional matrices. Comput. Math. Appl. 2008, 56: 1580–1586. 10.1016/j.camwa.2008.03.007 Mursaleen M, Mohiuddine SA: On σ -conservative and boundedly σ -conservative four-dimensional matrices. Comput. Math. Appl. 2010, 59: 880–885. 10.1016/j.camwa.2009.10.006 Mursaleen M: Almost strongly regular matrices and a core theorem for double sequences. J. Math. Anal. Appl. 2004,293(2):523–531. 10.1016/j.jmaa.2004.01.014 Mursaleen M, Edely OHH: Almost convergence and a core theorem for double sequences. J. Math. Anal. Appl. 2004,293(2):532–540. 10.1016/j.jmaa.2004.01.015 Altay B, Başar F: Some new spaces of double sequences. J. Math. Anal. Appl. 2005, 309: 70–90. 10.1016/j.jmaa.2004.12.020 Başar F, Sever Y:The space L q of double sequences. Math. J. Okayama Univ. 2009, 51: 149–157. Mursaleen M, Mohiuddine SA: Some matrix transformations of convex and paranormed sequence spaces into the spaces of invariant means. J. Funct. Spaces Appl. 2012., 2012: Article ID 612671 Mohiuddine SA, Alotaibi A: Some spaces of double sequences obtained through invariant mean and related concepts. Abstr. Appl. Anal. 2013., 2013: Article ID 507950 Demirci K: Strong A -summability and A -statistical convergence. Indian J. Pure Appl. Math. 1996, 27: 589–593. Mursaleen M, Mohiuddine SA: Some new double sequences spaces of invariant means. Glas. Mat. 2010,45(65):139–153. Parashar SD, Choudhary B: Sequence spaces defined by Orlicz functions. Indian J. Pure Appl. Math. 1994, 25: 419–428. Kizmaz H: On certain sequences spaces. Can. Math. Bull. 1981,24(2):169–176. 10.4153/CMB-1981-027-5 Et M, Çolak R: On generalized difference sequence spaces. Soochow J. Math. 1995,21(4):377–386. Et M: Spaces of Cesàro difference sequences of order r defined by a modulus function in a locally convex space. Taiwan. J. Math. 2006,10(4):865–879. Et M: Generalized Cesàro difference sequence spaces of non-absolute type involving lacunary sequences. Appl. Math. Comput. 2013, 219: 9372–9376. 10.1016/j.amc.2013.03.039 Raj K, Sharma AK, Sharma SK: A sequence space defined by Musielak-Orlicz function. Int. J. Pure Appl. Math. 2011, 67: 475–484. Raj K, Jamwal S, Sharma SK: New classes of generalized sequence spaces defined by an Orlicz function. J. Comput. Anal. Appl. 2013, 15: 730–737. Raj K, Sharma SK: Some generalized difference double sequence spaces defined by a sequence of Orlicz-function. CUBO 2012, 14: 167–189. 10.4067/S0719-06462012000300011 Raj K, Sharma SK, Sharma AK: Some difference sequence spaces in n -normed spaces defined by Musielak-Orlicz function. Armen. J. Math. 2010, 3: 127–141. Tripathy BC: Generalized difference paranormed statistically convergent sequences defined by Orlicz function in a locally convex spaces. Soochow J. Math. 2004, 30: 431–446. Et M, Altin Y, Choudhary B, Tripathy BC: On some classes of sequences defined by sequences of Orlicz functions. Math. Inequal. Appl. 2006, 9: 335–342. Lindenstrauss J, Tzafriri L: On Orlicz sequence spaces. Isr. J. Math. 1971, 10: 379–390. 10.1007/BF02771656 Maligranda L Seminars in Mathematics 5. Orlicz Spaces and Interpolation 1989. Polish Academy of Science Musielak J Lecture Notes in Mathematics 1034. In Orlicz Spaces and Modular Spaces. Springer, Berlin; 1983. Pringsheim A: Zur theorie der zweifach unendlichen zahlenfolgen. Math. Ann. 1900, 53: 289–321. 10.1007/BF01448977 Cooke RG: Infinite Matrices and Sequence Spaces. Macmillan & Co., London; 1950. Robison GM: Divergent double sequences and series. Trans. Am. Math. Soc. 1926, 28: 50–73. 10.1090/S0002-9947-1926-1501332-5 Hamilton HJ: Transformation of multiple sequences. Duke Math. J. 1936, 2: 29–60. 10.1215/S0012-7094-36-00204-1 Maddox IJ: Elements of Functional Analysis. 2nd edition. Cambridge University Press, Cambridge; 1988. Simons S:The sequence spaces l( p v ) and m( p v ) . Proc. Lond. Math. Soc. 1965,15(3):422–436. Yurdakadim T, Tas E: Double sequences and Orlicz functions. Period. Math. Hung. 2013, 67: 47–54. 10.1007/s10998-013-6362-x Mohiuddine SA, Raj K, Alotaibi A: Some paranormed double difference sequence spaces for Orlicz functions and bounded-regular matrices. Abstr. Appl. Anal. 2014., 2014: Article ID 419064